Graph operations and neighbor-integrity

Alpay Kırlangıc

Displaying similar documents to “Graph operations and neighbor-integrity”

Minus total domination in graphs

Hua Ming Xing, Hai-Long Liu (2009)

Czechoslovak Mathematical Journal

Similarity:

A three-valued function $f V \to {- 1, 0, 1}$ defined on the vertices of a graph $G = (V, E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v \in V$ , $f (N (v)) \geq 1$ , where $N (v)$ consists of every vertex adjacent to $v$ . The weight of an MTDF is $f (V) = \sum f (v)$ , over all vertices $v \in V$ . The minus total domination number of a graph $G$ , denoted $γ_{t}^{-} (G)$ , equals the minimum weight of an MTDF of $G$ . In this paper, we discuss some properties of minus total domination on a graph...

On total restrained domination in graphs

De-xiang Ma, Xue-Gang Chen, Liang Sun (2005)

Czechoslovak Mathematical Journal

Similarity:

In this paper we initiate the study of total restrained domination in graphs. Let $G = (V, E)$ be a graph. A total restrained dominating set is a set $S \subseteq V$ where every vertex in $V - S$ is adjacent to a vertex in $S$ as well as to another vertex in $V - S$ , and every vertex in $S$ is adjacent to another vertex in $S$ . The total restrained domination number of $G$ , denoted by $γ_{r}^{t} (G)$ , is the smallest cardinality of a total restrained dominating set of $G$ . First, some exact values and sharp bounds for $γ_{r}^{t} (G)$ are given in Section 2....

On signed majority total domination in graphs

Hua Ming Xing, Liang Sun, Xue-Gang Chen (2005)

Czechoslovak Mathematical Journal

Similarity:

We initiate the study of signed majority total domination in graphs. Let $G = (V, E)$ be a simple graph. For any real valued function $f V \to ℝ$ and $S \subseteq V$ , let $f (S) = \sum_{v \in S} f (v)$ . A signed majority total dominating function is a function $f V \to {- 1, 1}$ such that $f (N (v)) \geq 1$ for at least a half of the vertices $v \in V$ . The signed majority total domination number of a graph $G$ is $γ_{m a j}^{t} (G) = min {f (V) ∣ f$ is a signed majority total dominating function on $G}$ . We research some properties of the signed majority total domination number of a graph $G$ and obtain a few lower bounds of $γ_{m a j}^{t} (G)$ . ...

The independent resolving number of a graph

Gary Chartrand, Varaporn Saenpholphat, Ping Zhang (2003)

Mathematica Bohemica

Similarity:

For an ordered set $W = {w_{1}, w_{2}, \dots, w_{k}}$ of vertices in a connected graph $G$ and a vertex $v$ of $G$ , the code of $v$ with respect to $W$ is the $k$ -vector $c_{W} (v) = (d (v, w_{1}), d (v, w_{2}), \dots, d (v, w_{k})) .$ The set $W$ is an independent resolving set for $G$ if (1) $W$ is independent in $G$ and (2) distinct vertices have distinct codes with respect to $W$ . The cardinality of a minimum independent resolving set in $G$ is the independent resolving number $i r (G)$ . We study the existence of independent resolving sets in graphs, characterize all nontrivial connected graphs $G$ of order...

Bounds concerning the alliance number

Grady Bullington, Linda Eroh, Steven J. Winters (2009)

Mathematica Bohemica

Similarity:

P. Kristiansen, S. M. Hedetniemi, and S. T. Hedetniemi, in Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004), 157–177, and T. W. Haynes, S. T. Hedetniemi, and M. A. Henning, in Global defensive alliances in graphs, Electron. J. Combin. 10 (2003), introduced the defensive alliance number $a (G)$ , strong defensive alliance number $\hat{a} (G)$ , and global defensive alliance number $γ_{a} (G)$ . In this paper, we consider relationships between these parameters and the domination number $γ (G)$ . For any positive...